The classical helicity within a volume \(V\)  would be defined as \(h(V) = \int _V {\bf A} \cdot {\bf B} \, dV, \)  where \({\bf A}\)  is the vector potential of \({\bf B}\) . This quantity is dependent in general on the gauge of \({\bf A}\) , and so we use the alternative relative helicity instead [1]}. In a 3D domain, this would be calculated by finding a potential field \({\bf B}_P\)  matching the original magnetic field on the boundary, and a corresponding vector potential, \({\bf A}_P\) . The relative helicity would then be
\(H_R = \int _V ({\bf A + A}_P) \cdot ({\bf B - B}_P) \, dV.\) 
